Developmental Math—An Open Program
Instructor Guide
Unit 2 – Table of Contents
Unit 2: Fractions and Mixed Numbers
Learning Objectives
2.2
Instructor Notes
2.4



The Mathematics of Fractions and Mixed Numbers
Teaching Tips: Challenges and Approaches
Additional Resources
Instructor Overview

2.11
Tutor Simulation: Increasing the Size of a Recipe
Instructor Overview

2.12
Puzzle: Fraction Matchin'
Instructor Overview

2.14
Project: Let's Get Cooking!
Common Core Standards
2.21
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Monterey Institute for Technology and Education (MITE) 2012
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2.1
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Learning Objectives
Unit 2: Fractions and Mixed Numbers
Lesson 1: Introduction to Fractions and Mixed Numbers
Topic 1: Introduction to Fractions and Mixed Numbers
Learning Objectives
 Identify the numerator and denominator of a fraction.
 Represent a fraction as part of a whole or part of a set.
Topic 2: Proper and Improper Fractions
Learning Objectives
 Identify proper and improper fractions.
 Change improper fractions to mixed numbers.
 Change mixed numbers to improper fractions.
Topic 3: Factors and Primes
Learning Objectives
 Recognize (by using the divisibility rule) if a number is divisible by 2, 3, 4, 5, 6,
9, or 10.
 Find the factors of a number.
 Determine whether a number is prime, composite, or neither.
 Find the prime factorization of a number.
Topic 4: Simplifying Fractions
Learning Objectives
 Find an equivalent fraction with a given denominator.
 Simplify a fraction to lowest terms.
Topic 5: Comparing Fractions
Learning Objectives
 Determine whether two fractions are equivalent.
 Use > or < to compare fractions.
Lesson 2: Multiplying and Dividing Fractions and Mixed Numbers
Topic 1: Multiplying Fractions and Mixed Numbers
Learning Objectives
 Multiply two or more fractions.
 Multiply a fraction by a whole number.
 Multiply two or more mixed numbers.
 Solve application problems that require multiplication of fractions or mixed
numbers.
2.2
Developmental Math—An Open Program
Instructor Guide
Topic 2: Dividing Fractions and Mixed Numbers
Learning Objectives
 Find the reciprocal of a number.
 Divide two fractions.
 Divide two mixed numbers.
 Divide fractions, mixed numbers, and whole numbers.
 Solve application problems that require division of fractions or mixed
numbers.
Lesson 3: Adding and Subtracting Fractions and Mixed Numbers
Topic 1: Adding Fractions and Mixed Numbers
Learning Objectives
 Add fractions with like denominators.
 Find the least common multiple (LCM) of two or more numbers.
 Find the common denominator of fractions with unlike denominators.
 Add fractions with unlike denominators.
 Add mixed numbers with like and unlike denominators.
 Solve application problems that require the addition of fractions or mixed
numbers.
Topic 2: Subtracting Fractions and Mixed Numbers
Learning Objectives
 Subtract fractions with like and unlike denominators.
 Subtract mixed numbers without regrouping.
 Subtract mixed numbers with regrouping.
 Solve application problems that require the subtraction of fractions or mixed
numbers.
2.3
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Instructor Notes
Unit 2: Fractions and Mixed Numbers
Instructor Notes
The Mathematics of Fractions and Mixed Numbers
This unit tackles one of the most disliked topics in basic mathematics—fractions. As much as
students will want to avoid them, fractions will crop up in every part of this and every other math
course and are surprisingly common in the outside world as well.
By the time they've finished Unit 2, students will be well on their way to accepting, perhaps even
appreciating, fractions. They'll know the terminology of fractions and how to simplify, compare,
add, subtract, multiply, and divide these kinds of numbers. They'll also have seen numerous
examples of the application of fractions to real-life situations.
Teaching Tips: Challenges and Approaches
Fear of Fractions
The main challenge in teaching fractions is simply overcoming your students' almost universal
fear of them. Fractions look complicated and can't easily be punched into a standard calculator,
so to most developmental math students, they'll seem to be far more trouble than they're worth.
The best way to overcome this reluctance to deal with fractions is to tie them into everyday
experiences—familiarity breeds confidence. If students understand where fractions are going to
be encountered and how they are relevant, they'll be more eager to understand them.
For example, one of the most common uses of fractions is in cooking and recipes—all your
students have eaten, and many of them have cooked. So in the topic texts for this unit we often
use food-related examples to define terms and illustrate fraction problems. First, a measuring
cup reminds students what fractions are:
2.4
Developmental Math—An Open Program
Instructor Guide
[From Lesson 1, Topic 1, Topic Text]
Later, pizzas are used to help define improper fractions and mixed numbers:
[From Lesson 1, Topic 2, Topic Text]
2.5
Developmental Math—An Open Program
Instructor Guide
Relating fractions to common and comfortable situations like these reassures students that
learning about fractions is neither frightening nor foolish.
Divisibility Rules
Even after students get over their reluctance, some will have trouble carrying out calculations
with fractions. Finding common denominators and adding and subtracting fractions are the most
challenging issues.
We suggest reviewing the divisibility rules before tackling these procedures. The divisibility rules
for 2, 3, 4, 5, 6, 9 and 10 make it much easier to simplify fractions and will also help students
find common denominators quickly. The rules are explained and illustrated this way in the
course:
[From Lesson 1, Topic 3, Topic Text]
Common Denominators
Common denominators must be found to compare, add, and subtract fractions. Most students
can do this fairly easily when the denominators are small, such as 3 and 4 or 4 and 6. But, what
2.6
Developmental Math—An Open Program
Instructor Guide
if the denominators are larger, like 12 and 15? Many students cannot sift through this problem
in their heads. We suggest providing students with several alternate methods for finding
common denominators: using the divisibility rules, listing multiples of each denominator, and
finding the prime factorizations.
Operations
The hardest challenge is likely to be adding and subtracting fractions. In the past, students
learned how to first add, then subtract, multiply and finally divide fractions, in the same order
they learned to carry out these operations with whole numbers.
Currently, the practice is to teach multiplication and division of fractions before addition and
subtraction. Multiplication and division are easier because there's no need to find a common
denominator. In this course, we follow this new sequence. Once students are adept at doing a
few operations on fractions, learning the last two procedures won't be quite so intimidating.
Multiplication of fractions is definitely the easiest of the four basic operations. Be sure to explain
that students should simplify fractions and convert mixed numbers to improper fractions before
multiplying. Remind them that a whole number can be turned into a fraction by putting it over
one without changing its value.
Once students understand how to multiply with fractions, they'll have little trouble with division,
since these problems can also be solved by multiplying. Just teach them a phrase like “keep –
change – flip” to help them remember how (keep the first fraction (or mixed or whole number),
change the division sign to a multiplication sign, and flip the second fraction). It can be helpful
to remind students that they will need to put a whole number over one before finding the
reciprocal (i.e. flipping). Also, a mixed number will need to be converted to an improper fraction
before finding the reciprocal. Some students will say that the reciprocal of 2
8
3
is 2 —you
8
3
can’t just “flip” the fractional part of the mixed number.
Students generally have the most difficulty with adding and subtracting fractions. In a problem
with like denominators, some will want to add both the numerators and denominators. You can
point out that two apples added to five apples is seven apples. No matter how many apples you
add, they're still apples. Similarly, two-ninths added to five-ninths is seven-ninths, not seveneighteenths, because no matter how many ninths you add, they're still ninths.
When unlike denominators appear, some students will again try to solve these problems by
adding both the numerators and the denominators. Others will struggle to find common
denominators. Encourage them first to work with the divisibility rules or factorization. Some
students have learned to find a common denominator by multiplying all the denominators in the
problem together. This is okay to do, but then the answer will likely need to be simplified, a step
that students often forget.
2.7
Developmental Math—An Open Program
Instructor Guide
The same overall techniques for addition of fractions apply to subtraction—find a common
denominator, convert the fractions to this common denominator form, and then subtract the
numerators. But there is a good chance some regrouping might have to be done. This
regrouping process, for example renaming 8 as 7
5
2
8
or 6 as 5 , needs to be explained—in
3
3
8
fact, it is beneficial to give a series of examples of regrouping before even getting to a
subtraction problem.
An unfortunate result of teaching students that common denominators are needed to add or
subtract fractions is that they then try to use them when the next multiplication or division
problem comes along. A reminder that common denominators are not needed when multiplying
or dividing fractions might be necessary.
Keep In Mind
All students will have studied fractions before. One thing that can be counted on with
developmental students is that if they haven’t used fractions for any length of time, their skills
will be rusty. Typically they will also recall not liking fractions and they will avoid using them
whenever possible. When the study of algebra is started and the answer to an algebraic
equation is “ x 
1
”, you can count on getting the answer “ x  .14 ”. Why? Students are just
7
more comfortable with decimals as compared to fractions. At this point, it must be explained to
students that “ x 
1
” and “ x  .14 ” are not equivalent answers.
7
Students sometimes confuse the numerator and denominator of a fraction. Pointing out that
“denominator” and “down” both begin with “d” may help.
In this course, improper fractions should be simplified to either whole or mixed numbers. It
should be noted that because proper fractions have a numerator that's less than the
denominator, this means a fraction equivalent to 1, like
7
, is an improper fraction.
7
Remind students to check that all their fractions are behaving "properly" by making sure that an
improper fraction is not left as a final answer. In every problem presented in the course
materials, students will see that answers are simplified:
2.8
Developmental Math—An Open Program
Instructor Guide
[From Lesson 2, Topic 1, Presentation]
It may help students to understand how to convert improper fractions to mixed numbers by
pointing out that the process is just a division problem:
[From Lesson 2, Topic 1, Topic Text]
2.9
Developmental Math—An Open Program
Instructor Guide
Additional Resources
In all mathematics, the best way to really learn new skills and ideas is repetition. Problem
solving is woven into every aspect of this course—each topic includes warm-up, practice, and
review problems for students to solve on their own. The presentations, worked examples, and
topic texts demonstrate how to tackle even more problems. But practice makes perfect, and
some students will benefit from additional work.
A good website to review all the skills learned in this unit can be found at
http://www.aaastudy.com/fra.htm. After a brief review, an applet tests knowledge on many
different fraction topics.
Practice with simplifying and comparing fractions can be found at
http://www.learningplanet.com/sam/ff/index.asp and more help can be found at
http://www.visualfractions.com/CompareL/comparel.html for comparing fractions.
Knowing factors will help students find common denominators. A good practice for factor trees
(which are obtained from the prime factors of a number) can be found at http://www.cut-theknot.org/Curriculum/Arithmetic/BTreeTesting.shtml.
Summary
The goal of this unit is to help students get over their fear of fractions and learn how to work with
these numbers. After completing these lessons, they'll know how to simplify, add, subtract,
multiply, and divide fractions. Students will understand and appreciate fractions more easily if
they're shown how frequently their knowledge of fractions can be used in everyday life.
2.10
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Tutor Simulation
Unit 2: Fractions and Mixed Numbers
Instructor Overview
Tutor Simulation: Increasing the Size of a Recipe
Purpose
This simulation allows students to demonstrate their understanding of fractions and mixed
numbers. Students will be asked to apply what they have learned to solve a problem involving:




Adding Fractions
Multiplying Fractions
Dividing Fractions
Applying Fractions to Real-World Situations
Problem
Students are presented with the following problem:
You are working part-time in a bakery. You have to bake a lot of loaves of bread, but the recipes
only give the ingredient amounts for one loaf. Your challenge will be to work with the fractions in
the bread recipes and figure out the ingredients you'll need to bake multiple loaves.
Recommendations
Tutor simulations are designed to give students a chance to assess their understanding of unit
material in a personal, risk-free situation. Before directing students to the simulation,



make sure they have completed all other unit material
explain the mechanics of tutor simulations
o Students will be given a problem and then guided through its solution by a video
tutor;
o After each answer is chosen, students should wait for tutor feedback before
continuing;
o After the simulation is completed, students will be given an assessment of their
efforts. If areas of concern are found, the students should review unit materials or
seek help from their instructor.
emphasize that this is an exploration, not an exam
2.11
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Puzzle
Unit 2: Fractions and Mixed Numbers
Instructor Overview
Puzzle: Fraction Matchin'
Objectives
Fraction Matchin' is a puzzle that mixes numerical and visual representations of fractions. The
game tests a player's ability to recognize various forms of fractions and to convert mixed
numbers into improper fractions.
Figure 1. Players pick the pair of pie and shaded rectangle charts that match the central fraction.
2.12
Developmental Math—An Open Program
Instructor Guide
Description
This puzzle has three levels, each with 10 games. Every game begins with a fraction in numeric
form, surrounded by pie charts and shaded rectangle graphs. Players must pick the pair of
graphs that represent the same value as the center fraction. In the 1st level, all given fractions
are simple. In the 2nd level, all fractions are improper. In the 3rd level, mixed numbers are used.
Players earn points by picking the correct pairs. Play does not proceed until the pairs are
matched.
Fraction Matchin' is suitable for both individual, group, and classroom play.
2.13
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Project
Unit 2: Fractions and Mixed Numbers
Instructor Overview
Project: Let's Get Cooking!
Student Instructions
Introduction
Fractions are a large part of baking. Ingredient measurements are often given in quarter cup
increments. In fact, small measurements are sometimes given in eighths of a teaspoon. In
order to successfully bake, it is important to be able to work with fractions. Recipes will need to
be doubled or halved depending on the quantity that needs to be made. Baking, therefore,
requires an understanding of fractions. When you can work effortlessly with fractions you have
the skills to bake up whatever you are in the mood for. Who doesn’t like a warm chocolate chip
cookie now and then?
Task
You are having a get together and are expecting 30 guests. You plan on serving Banana
Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with
your group to create recipe cards to feed 30 people. Next, total up the ingredients needed.
Then, check to see how much of each product needs to be purchased based on what is already
on hand. Finally, create a display of your project that showcases your group’s creativity.
Instructions
Complete each problem in order. Be sure to keep careful notes and save your work as you
progress. You will work together to create a display at the end of the project.
1. Use your knowledge of fractions to re-write the recipe for Banana Bread. The card states
that it serves 10 people. What will need to be done in order to make enough bread for 30
people? Show your work neatly and then re-write the recipe card.
2.14
Developmental Math—An Open Program
Instructor Guide
2. Use your knowledge of fractions to re-write the recipe for Chocolate Chip Cookies. The card
states that it makes 60 cookies. What will need to be done in order to make 30 cookies?
Show your work neatly and then re-write the recipe card.
2.15
Developmental Math—An Open Program
Instructor Guide
3. Use your knowledge of fractions to re-write the recipe for Sugar Cookies. The card states
that it serves 20 people. What will need to be done in order to make enough to serve 30
people? Show your work neatly and then re-write the recipe card.
4. Use your new recipe cards to find the total amount of each ingredient needed. Use the table
below to help you.
Ingredient
Recipe 1 + 2 + 3
(Don’t forget to find common denominators
before adding.)
Flour
Sugar
Butter
Vanilla
Baking Soda
Eggs
Salt
Chocolate Chips
Bananas
2.16
Total needed
(Be sure to simplify
any fractions.)
Developmental Math—An Open Program
Instructor Guide
5. When taking inventory in the pantry, you found that you already have some of the
ingredients. Use the following table to organize your work. Don’t forget common
denominators.
HINT: If you need 5 eggs and you already have 2, how many do you need to buy? Write a
number sentence to describe this situation. Which operation did you use? Use the same
method to solve for the other ingredients. Don’t forget common denominators.
Ingredient
Total needed from above
Already in Pantry
Flour
1
3 cups
2
Sugar
2 cups
Butter
3
cup
4
Vanilla
2 teaspoons
Baking Soda
1
1 teaspoons
2
Eggs
2
Salt
1 teaspoon
Chocolate Chips
1
pound
4
Bananas
4
Needs to be bought
Collaboration
Compare your three recipe cards with another group. The cards should look identical. If a
measured ingredient varies, look at the work to determine where the error was made. Then
compare the table with total ingredients. Again, the table should look identical. Compare your
work to find any errors. Finally, compare the last table. Do the answers agree? Are all
fractions simplified?
2.17
Developmental Math—An Open Program
Instructor Guide
Conclusion
Create a poster to display your work. Include the three new recipe cards, as well as the math
work done to figure each new amount. Then include the table with the ingredient totals and the
table with the amount to be purchased. Again, include the math on the poster. Finally,
incorporate pictures and color to the poster to create a professional looking product.
Instructor Notes
Assignment Procedures
Problem 2
This is a prime opportunity to discuss that dividing by two and multiplying by
1
are equivalent
2
operations. Which operation will be the easiest and most reliable to perform? It depends on the
situation and the student. 4 divided by 2 seems easier than multiplying by
can be more difficult for some students than
3
1
; however,  2
4
2
3 1
 . Understanding that the operations are
4 2
equivalent can allow students to be more successful with fractions.
Problem 3
Students may choose multiple methods to re-write this recipe card. They could multiply by
they could multiply by
3
or
2
1
and then add the original amount. If time allows, discuss the multiple
2
methods. Which method did the group choose? Why?
Recommendations




Have students work in teams to encourage brainstorming and cooperative learning.
Assign a specific timeline for completion of the project that includes milestone dates.
Provide students feedback as they complete each milestone.
Ensure that each member of student groups has a specific job.
Technology Integration
This project provides abundant opportunities for technology integration, and gives students the
chance to research and collaborate using online technology. The students’ instructions list
several websites that provide information on numbering systems, game design, and graphics.
2.18
Developmental Math—An Open Program
Instructor Guide
The following are other examples of free Internet resources that can be used to support this
project:
http://www.moodle.org
An Open Source Course Management System (CMS), also known as a Learning Management
System (LMS) or a Virtual Learning Environment (VLE). Moodle has become very popular
among educators around the world as a tool for creating online dynamic websites for their
students.
http://www.wikispaces.com/site/for/teachers or http://pbworks.com/content/edu+overview
Allows you to create a secure online Wiki workspace in about 60 seconds. Encourage
classroom participation with interactive Wiki pages that students can view and edit from any
computer. Share class resources and completed student work with parents.
http://www.docs.google.com
Allows students to collaborate in real-time from any computer. Google Docs provides free
access and storage for word processing, spreadsheets, presentations, and surveys. This is
ideal for group projects.
http://why.openoffice.org/
The leading open-source office software suite for word processing, spreadsheets,
presentations, graphics, databases and more. It can read and write files from other common
office software packages like Microsoft Word or Excel and MacWorks. It can be downloaded
and used completely free of charge for any purpose.
Rubric
Score
Content
•
•
4
•
•
Presentation/Communication
The solution shows a deep understanding of
the problem including the ability to identify
the appropriate mathematical concepts and
the information necessary for its solution.
The solution completely addresses all
mathematical components presented in the
task.
The solution puts to use the underlying
mathematical concepts upon which the task
is designed and applies procedures
accurately to correctly solve the problem
and verify the results.
Mathematically relevant observations and/or
connections are made.
2.19
•
•
•
•
There is a clear, effective explanation
detailing how the problem is solved.
All of the steps are included so that
the reader does not need to infer
how and why decisions were made.
Mathematical representation is
actively used as a means of
communicating ideas related to the
solution of the problem.
There is precise and appropriate use
of mathematical terminology and
notation.
Your project is professional looking
with graphics and effective use of
color.
Developmental Math—An Open Program
Instructor Guide
•
•
3
•
•
•
•
2
•
•
•
•
1
•
•
The solution shows that the student has a
broad understanding of the problem and the
major concepts necessary for its solution.
The solution addresses all of the
mathematical components presented in the
task.
The student uses a strategy that includes
mathematical procedures and some
mathematical reasoning that leads to a
solution of the problem.
Most parts of the project are correct with
only minor mathematical errors.
The solution is not complete indicating that
parts of the problem are not understood.
The solution addresses some, but not all of
the mathematical components presented in
the task.
The student uses a strategy that is partially
useful, and demonstrates some evidence of
mathematical reasoning.
Some parts of the project may be correct,
but major errors are noted and the student
could not completely carry out mathematical
procedures.
There is no solution, or the solution has no
relationship to the task.
No evidence of a strategy, procedure, or
mathematical reasoning and/or uses a
strategy that does not help solve the
problem.
The solution addresses none of the
mathematical components presented in the
task.
There were so many errors in mathematical
procedures that the problem could not be
solved.
2.20
•
•
•
•
•
•
•
•
•
•
•
•
There is a clear explanation.
There is appropriate use of accurate
mathematical representation.
There is effective use of
mathematical terminology and
notation.
Your project is neat with graphics
and effective use of color.
Your project is hard to follow
because the material is presented in
a manner that jumps around between
unconnected topics.
There is some use of appropriate
mathematical representation.
There is some use of mathematical
terminology and notation appropriate
to the problem.
Your project contains low quality
graphics and colors that do not add
interest to the project.
There is no explanation of the
solution, the explanation cannot be
understood or it is unrelated to the
problem.
There is no use or inappropriate use
of mathematical representations (e.g.
figures, diagrams, graphs, tables,
etc.).
There is no use, or mostly
inappropriate use, of mathematical
terminology and notation.
Your project is missing graphics and
uses little to no color.
Developmental Math—An Open Program
Instructor Guide
Unit 2 – Correlation to Common Core
Standards
Learning Objectives
Unit 2: Fractions and Mixed Numbers
Common Core Standards
Unit 2, Lesson 1, Topic 1: Introduction to Fractions and Mixed Numbers
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
Construct viable arguments and
critique the reasoning of others.
CATEGORY / CLUSTER
MP.8.5.
Use appropriate tools strategically.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
CATEGORY / CLUSTER
MP-5.
Use appropriate tools strategically.
Unit 2, Lesson 1, Topic 2: Proper and Improper Fractions
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 1, Topic 3: Factors and Primes
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
2.21
Developmental Math—An Open Program
Instructor Guide
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 1, Topic 4: Simplifying Fractions
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 1, Topic 5: Comparing Fractions
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 2, Topic 1: Multiplying Fractions and Mixed Numbers
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
Construct viable arguments and
critique the reasoning of others.
2.22
Developmental Math—An Open Program
Instructor Guide
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 2, Topic 2: Dividing Fractions and Mixed Numbers
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 3, Topic 1: Adding Fractions and Mixed Numbers
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
Unit 2, Lesson 3, Topic 2: Subtracting Fractions and Mixed Numbers
STRAND / DOMAIN
Grade: 8 - Adopted 2010
CC.MP.8.
Mathematical Practices
CATEGORY / CLUSTER
MP.8.3.
STRAND / DOMAIN
Grade: 9-12 - Adopted 2010
CC.MP.
Mathematical Practices
CATEGORY / CLUSTER
MP-3.
Construct viable arguments and
critique the reasoning of others.
Construct viable arguments and
critique the reasoning of others.
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